Even in Washington, it is rare to see two such momentous state visits - one by the leader of the world's most populous country and the other by the head of one of the world's most influential religions - coincide so closely. Yet despite being on US soil at the same time, President Xi Jinping and Pope Francis will miss each other by the slimmest of margins - not once, but twice. Yesterday, shortly before Xi arrived in Washington to be met by US Vice-President Joe Biden and his wife Jill, Francis was leaving town, heading for New York to address the United Nations General Assembly. Tomorrow, when Xi arrives to address the UN, the pope will be on his way to Philadelphia. READ MORE: Xi's state visit to the US The visits have prompted comparisons between the two and discussions on Sino-Vatican relations, strained since Mao Zedong severed ties in 1951. The Washington Post said Francis was "riding a wave of popularity unmatched by his recent predecessors, a religious figure renowned for his common touch", while Xi was "an authoritarian leader who has cracked down on free expression". While the overlapping visits are unprecedented, experts are not surprised the pair chose to miss each other. Ties between China and the Vatican remain strained despite efforts to ease them. After Xi and Francis assumed office within hours of one another in 2013, the two exchanged letters of congratulations and the Vatican is believed to have reached out to Beijing to resume dialogue. China allowed Francis to fly across its airspace last year, and the pope extended goodwill by sending telegrams to Xi. Yet myriad conflicts - from Beijing's crackdown on churches to disagreements over who has the authority to appoint bishops - block the path to the establishment of diplomatic ties. Sister Beatrice Leung Kit-fun, research professor at Taiwan's Wenzao Ursuline University of Languages, said relations with the Vatican were not a high priority for Beijing, as it was preoccupied with issues like cybersecurity, conflicts in the South China Sea and economic restructuring. "It's not the right time. China has undergone a political struggle - Xi Jinping is very much aware that if he gave more concessions [to the Vatican] he would be attacked by his opposition," said Leung. "Right now, the political landscape is severe." Roland Vogt, assistant professor of European studies at the University of Hong Kong, said the Vatican was the only western European state without diplomatic ties with China. To do so, it needed to break its ties to Taiwan. It's not the right time...Right now, the political landscape is severe Sister Beatrice Leung Kit-fun, research professor Yet China stands to benefit from stronger relations with the Vatican. The Vatican could act as a mediator between China and other countries, offering its services to deal with territorial disputes, Vogt said, while Leung said that aligning with the pope could improve China's image and strengthen its "soft power". "There's some overlap between the interests of the Vatican and those of China," Vogt said. "But when it comes to domestic life, to Catholicism in China, there are still a lot of obstacles." The White House invited reporters covering the pope's trip to stay on to cover Xi's arrival.